Stock markets are complex systems, and traditional methods don't give good results when studying them. By using fractal and multi-fractal analysis, researchers can understand stock market dynamics and trends. The study looked at Germany, France, UK, and China stock markets from 2010 to 2019. The Hurst coefficient values show that Germany, France, and China markets are persistent, while the UK market is anti-persistent. This means China's market is stable and attractive to investors, while the UK market is risky. Multi-fractal analysis helped refine these findings and track market changes over time, including the impact of global crises and Brexit on market states. The methods used in the study are useful for evaluating stock markets, identifying trends, monitoring, and predicting market behavior.